FileVault is a built-in tool for encrypting data on a Macintosh computer. It was introduced in OS X 10.3 and was revised to FileVault 2 in 10.7. The original FileVault encrypted just the users’ home directories whereas FileVault 2 encrypts the entire startup disk. I generally only encourage customers to use Filevault 2 if the person knows exactly what Filevault 2 does, how it works, and if they have sensitive data on their machine.
When Filevault 2 is enabled on a Macintosh, the user is prompted to create a master password for the computer. If the password for that user is lost or forgotten, that master password can be used to decrypt your files instead. This is where things can get tricky because it is possible for your Filevault 2 password to be different from your user login password. This can then cause an issue where you try to reset your user password, and are then prompted for a Filevault password which you have since forgotten. Apple has done a great job at encrypting the startup disk and as far as I know cannot be reset without the password or recovery key.
So in short, if you see the FileVault setup screen when updating or installing OS X (pictured above) think twice about leaving these boxes checked (they are now selected by default on Yosemite 10.10 and higher). I am simply suggesting that you read about FileVault 2 and only enable it if you feel you need it. And if you enable it, keep you Master Password and/or recovery key in a safe place, preferably two safe places, and definitely NOT on the computer itself. Remember, with Filevault 2 off, your Macintosh is still password protected, just not encrypted, and this is a sufficient level of security for many users.